Catastrophic heart rhythm disturbances are among the leading causes of death in the United States. The most dangerous of these disturbances is ventricular fibrillation, a disturbance in which disordered wave propagation causes a fatal disruption of the synchronous contraction of the ventricle. A beat-to-beat alternation in the action potential duration (APD) of myocytes, i.e. alternans, is believed to be a direct precursor of ventricular fibrillation in the whole heart.
A common approach for the prediction of alternans is to construct the restitution curve, which is the nonlinear functional relationship between the APD and the preceding diastolic interval (DI). It has been proposed that alternans appears when the magnitude of the slope of the restitution curve exceeds one, known as the restitution hypothesis. However, this restitution hypothesis was derived under the assumption of periodic stimulation, when there is a dependence of the DI on the immediate preceding APD (i.e. feedback). In addition, under physiological conditions, the heart rate exhibits substantial variations in time, known as heart rate variability (HRV), which introduces deviations from periodic stimulation in the system.